0195136047.pdf

PROBLEMS 53

The resistance of a conductor with a circular cross-sectional areaA, lengthl, and conductivity

σis given by Equation (1.2.2),

R=

l

σA

Depending on the compression or elongation as a consequence of an external force, the length

changes, and hence the resistance changes. The relationship between those changes is given by

the gauge factorG,

G=

R/R

l/ l

in which the factorl/ l, the fractional change in length of an object, is known as the strain.

Alternatively, the change in resistance due to an applied strainε(=l/ l)is given by

R=R 0 Gε

whereR 0 is the zero-strain resistance, that is, the resistance of the strain gauge under no strain.

A typical gauge hasR 0 = 350 andG=2. Then for a strain of 1%, the change in resistance is

R= 7 . A Wheatstone bridge as presented in Section 1.4 is usually employed to measure the

small resistance changes associated with precise strain determination.

A typical strain gauge, shown in Figure 1.7.1, consists of a metal foil (such as nickel–copper

alloy) which is formed by a photoetching process in multiple conductors aligned with the direction

of the strain to be measured. The conductors are usually bonded to a thin backing made out of

a tough flexible plastic. The backing film, in turn, is attached to the test structure by a suitable

adhesive.

Metal foil

R

Copper-plated solder tabs

for electrical connections

Flexible plastic

backing film

Direction of

strain to

be measured

Figure 1.7.1Resistance strain gauge and circuit

symbol.

1

Problems

1.1.1Consider two 1-C charges separated by1minfree

space. Show that the force exerted on each is about

one million tons.

*1.1.2Point charges, each of

√

4 πε 0 C, are located at

the vertices of an equilateral triangle of sidea.

Determine the electric force on each charge.

1.1.3Two charges of equal magnitude 5μCbut opposite

sign are separated by a distance of 10 m. Find

the net force experienced by a positive charge

*Complete solutions for problems marked with an asterisk can be found on the CD-ROM packaged with this book.

q= 2 μC that is placed midway between the two

charges.

1.1.4The electric field intensity due to a point charge in

free space is given to be

(− ̄ax− ̄ay+ ̄az)/

√

12V/mat( 0 , 0 , 1 )

and 6 a ̄zat( 2 , 2 , 0 )

Determine the location and the value of the point

charge.